Problem: A swimming pool is open for $7\dfrac12$ hours during a day. The pool keeps one lifeguard on duty at a time, and each lifeguard's shift is $1\dfrac12$ hours long. How many shifts are there per day?
Explanation: We can think about this problem like this: $ {\text{number of shifts}} = {\text{total hours pool is open}} \div {\text{length of each shift}}$ ${\text{?}} = {7\dfrac12 \text{hours}} \div {1\dfrac{1}{2} \text{hours}}$ $\phantom{?} = {\dfrac{15}{2} \text{hours}} \div {\dfrac{3}{2} \text{hours}} ~~~~~~~{\text{Rewrite } {7\dfrac12} \text{ as } { \dfrac{15}{2}} \text{ and }{1\dfrac{1}{2}} \text{ as } {\dfrac{3}{2}}}$ $\phantom{?} = {\dfrac{15}{2}} \times \dfrac{2}{3} ~~~~~~~{\text{Rewrite dividing by} {\dfrac{3}{2}} \text{ as multiplying by} \dfrac{2}{3}}$ $\phantom{?} =\dfrac{15 \times 2}{2 \times 3}$ $\phantom{?} =\dfrac{30}{6}$ $\phantom{?} = {5 \text{ shifts}}$ There are $5$ shifts per day.